Errors introduced by lbw hybrid

july,2001

The native polarization of the lband wide hybrid
is linear. A switchable 90 deg hybrid has been placed after the dewar to
convert these signals to circular polarization. When this mode is used,
there is a potential error caused by the imbalance in amplitude and phase
of the two signals (linear polarization) being input to the hybrid.

Some math..

For computation purposes assume we input a monochromatic signal into both
inputs of the hybrid but let the signal have possibly different amplitudes
and a relative phase error.

The first thing to notice is that if eps = 0, then the two outputs are
equal, even if the input amplitudes vary.

How the hybrid can cause problems with the lwide receiver.

For eps to be non-zero, the signal input to the hybrid must be partially
polarized (or else you couldn't define eps which is a phase relationship
between polA and polB). This can occur if the RF signal is polarized or
a correlated cal (single diode) is used.

The cal diodes used for calibration have been measured with the hybrid
out. When the hybrid is switched in the routines will average the two cal
values. This assumes that the hybrid has combined the two inputs with no
phase errors. If two diodes are being used then there is no phase error
since eps is not defined. When a single diode is used (correlated cal..
eg. the calibration button on the gui) then eps is defined and the output
cal value in the two channels will vary depending on the phase error eps.

Figure 1. The power ratio of the hybrid outputs versus the phase error
eps.

The y axis is the power ratio of the hybrid outputs. The x
axis is the phase error in degrees. The different colors show the values
for different input power ratios. If you have a phase error of 20 degrees
then the output power ratio will be a factor of two different (while the
input power ratio was equal).

Figure 2. Lbw Cal/Tsys when using two separate diodes.

5 second cal on/offs were done at 1175,1300,1375, and 1415
Mhz using the correlator. The calDeflection/TsysDeflection is plotted versus
frequency. Solid lines are polA and dashed lines are polB. The black lines
are with the hybrid out. There is a difference in the two because the diodes
are different. The red lines are the measured values with the hybrid in.
The blue line is the expected value which is just the average of the two
cal input values. Since there are two diodes, there is no phase error and
the measured values lie quite close to the expected values.

Figure 3. Lbw Cal/Tsys when using a single diode for both polarization's.

This is the same measurement but now a single diode is split
and then injected into both polarizations. The black lines are with the
hybrid out. They differ by a small amount because the losses in the
two lines are not equal. The blue is what we expect the hybrid to
give: the average of the two inputs. The red lines show the values that
are measured. They differ from the expected values by +/- 25%. Using the
dual diodes, the system temperature for the two outputs is within 1K of
each other so this difference is the cals and not Tsys.

Figure 4.Lbw Cal/Tsys 1 diode and the computed phase error.

The black lines show the measured cal values using a single
diode and the hybrid. The blue line is what we expected them to be. The
red lines are the computed values using a phase error of 16.4 degrees and
an input amplitude ratio equal to the cal ratio measured when the
hybrid was out. The agreement is excellent. The frequency dependence is
because the 16.4 degree phase error was assumed to be caused by a path
difference at 1415 Mhz. As you move to lower frequency this becomes a proportionally
smaller phase error.

The 16.4 degree phase error corresponds to 16.4/360*3e10/1415e6= .97 cm
path difference. For a given frequency of observation you should be able
to divide your wavelength into this length and then use the fraction of
360 deg as your phase error. Lookup the value in figure 1 to see
what the ratio of the output powers will be.

Carl heiles measured a phase difference of 2.3 degrees between the cals
at their injection point (the cal directional coupler). This means that
the 16.4 +/- 2.3 degree error is between the cal injection point and the
output of the 90 degree hybrid (it includes any hybrid errors).

f you are going to use the lwide system in circular mode and you aren't
measuring polarized sources, then you should use 2 diodes (hcal) so that
the system temperatures you compute are reasonable.

If you use lbw with the hybrid in and you are interested in polarization
then you should probably use a single diode and use the cal measurement
to straighten out how the polarization of your source has been screwed
up by the hybrid. You won't be able to let the normal routines calibrate
your data since the cal values will be wrong.

If you are a "real astronomer" (see C. heiles A heuristic intro to radioastronomical
polarization, naic/nrao single dish workshop) then you would never use
the hybrid to start with !!!